Algebra 2Monday, 9/22/14 1.Warm-ups: pre-req skills needed for Chapter 2 (pg 57 #1-19 all)...
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Transcript of Algebra 2Monday, 9/22/14 1.Warm-ups: pre-req skills needed for Chapter 2 (pg 57 #1-19 all)...
Algebra 2 Monday, 9/22/141. Warm-ups: pre-req skills needed for Chapter 2 (pg 57 #1-19 all)
2. Discussion/Notes/Guided Practice: 2.1 Relations and Functions
3. HW: A#2.1 pages 62-63 #13-22 all; and #24-42 evens -- due Tues
UPCOMING QUIZ and TEST DATES:Wed 10/1: Quiz - Sections 2.1 - 2.4
WARM-UPS: Complete page 57 #1-19 allwrite your answers on this page
1. Identify the BIG Ideas for Chapter 2
2. Define key vocabulary terms for Section 2.1
3. Analyze and graph relations
4. Determine if a relation is a function
5. Determine if a graph is discrete or continuous
6. Understand and use the vertical line test to determine if a graph is a function
7. Find functional values
Success Criteria: Q&A, Guided Practice Problems, HW
Preview of Chapter 2Linear Relations and Functions
Use your textbook and identify the five “BIG Ideas” for Chapter 2:1.
2.
3.
4.
5.
Learning target #1
Preview of Chapter 2Linear Relations and Functions
1. Analyze relations and functions
2. Identify, graph, and write linear equations
3. Find the slope of a line
4. Draw scatter plots and find prediction equations
5. Graph special functions, linear inequalities, and absolute value inequalities
Vocabulary for this section – How many do you already know?
• Ordered pair:
• Cartesian coordinate plane:
• Quandrant:
• Relation:
• Domain:
• Range:
• Function:
• Mapping:
• One-to-one function:
• Discrete function:
• Continuous function:
• Vertical line test:
• Independent variable:
• Dependent variable:
• Function notation:
Learning target #2
• ________________: A pair of coordinates, written in the form (x, y), used to locate any point on a coordinate plane.
• ________________________: composed of the x-axis (horizontal) and y-axis (vertical), which meet at the origin (0, 0) and divide the plane into four quandrants.
Learning target #2
• Ordered Pair: A pair of coordinates, written in the form (x, y), used to locate any point on a coordinate plane.
• Cartesian Coordinate Plane: composed of the x-axis (horizontal) and y-axis (vertical), which meet at the origin (0, 0) and divide the plane into four quandrants.
Learning target #2
• ______________: is a set of ordered pairs.
• ______________ (of a relation): the set of all first coordinates (x-coordinates) from the ordered pairs.
• _____________ (of a relation): the set of all second coordinates (y-coordinates) from the order pairs.
Examples:
Learning targets #2 & 3
Relation; Domain; Range
• Relation: is a set of ordered pairs.
• Domain (of a relation): the set of all first coordinates (x-coordinates) from the ordered pairs.
• Range (of a relation): the set of all second coordinates (y-coordinates) from the order pairs.
Examples:• Relation:{ (12, 28), (15, 30), (8, 20), (12, 20), (20, 50)}
• Domain:{8, 12, 15, 20}
• Range:{20, 28, 30, 50}
Learning targets #2 & 3
Function
• A ___________ is a special type of relation. Each element of the domain is paired with exactly one element of the range.
• A ______________ shows how the members are paired. An example is shown to the right.
• The example to the right is a function; each element of the domain is paired with exactly one element of the domain. This is called a one-to-one function.
Functions can be represented as When speaking, we say “F of x” or “G of x”.
Learning targets #2 & 4
Function
• A ___________ is a special type of relation. Each element of the domain is paired with exactly one element of the range.
• A ______________ shows how the members are paired. An example is shown to the right.
• The example to the right is a function; each element of the domain is paired with exactly one element of the domain. This is called a one-to-one function.
• Relation:{(12, 28), (15, 30), (8, 20)}
Domain Range
Functions can be represented as When speaking, we say “F of x” or “G of x”.
Learning targets #2 & 4
12
15
8
28
30
20
Example #1
• State the domain and range of the relation . Draw a mapping. Is this relation a function?
Learning targets #1 - 4
Guided Practice – Example #1
• State the domain and range of the relation . Draw a mapping. Is this relation a function?
Learning targets #1 - 4
Also…try #1, 2, 3, and 8 on page 62
Practice Function or not?
-3
0
2
1
2
4
-1
1
4
3
5
-3
1
5
0
1
6
Domain Domain
Domain
Range Range
Range
Learning targets #2 & 4
Relations: Discrete or Continuous?Learning targets #2 & 5
Relations: Discrete or Continuous?
Discrete Continuous
Discrete graphs contain a set of points not connected.
Continuous graphs contain a smooth lineor curve.
Note: You can draw the graph of a continuous relationWithout lifting you pencil from the paper.
Learning targets #2 & 5
Vertical Line TestLearning targets #2 & 6
Vertical Line Test
• If no vertical line intersects a graph in more than one point, the graph represents a function.
• If some vertical line intersects a graph in two or more points, the graph DOES NOT represent a function.
Learning targets #2 & 6
Example #2
• The number if employees a company had in each year from 1999 to 2004 were 25, 28, 34, 31, 27, and 29. Graph this information and determine whether it represents a function. Is the relation discrete or continuous?
Learning targets #1 - 6
Example #3
• Graph the relation represented by .
• Find the domain and range.
• Determine if the relation is discrete or continuous.
• Determine whether the relation is a function.
Learning targets #1 - 6
Guided Practice – Examples #2&3
• Page 63 #4, 5, 6, 8, 9, and 10
Learning targets #1 - 6
Example #4
• Given , find each value.
a. b.
Learning target #7
Guided Practice – Example #4
1. Find if 2. Find if .
Learning target #7
A#2.1
pages 62-63
#13-22 all; and #24-42 evens
Due Tuesday!!!